What is the paper before this!? It looks interesting as well!
Samuel Butler was a 19th century English novelist, essayist and cri...
The estimation of energy consumption in the human brain is usually ...
## Jacquard Loom During the 1700s, a number of French weavers de...
For the sake of comparison about where we stand today: - Estimate ...
The all-or-none principle states that if a single neuron is stimula...
"Audrey" (Automatic Digit Recognition Unit) was a very early speec...
At the time of publishing of Shannon's paper it had only been 16 ye...
A traditional, or "deterministic" Turing machine, as described by A...
This is known as the halting problem. The halting problem is the pr...
Shannon is likely alluding to the following quote: > Everybody ta...
Hex is a strategy game played on a hexagonal grid. The goal is to c...
Nim is a strategic mathematical game where two players take turns r...
Checkers was one of the first non trivial games where machines were...
Shannon made significant contributions to the field of chess progra...
 *Claude Shannon and the These...
PROCEEDINGS
OF
THE
I.R.E.
It
will
be
seen
that
the
effect
of
expressing
approval
when
a
particular
figure
has
been
printed
is
to
increase
the
chance
of
that
figure
being
printed
on
subsequent
occasions,
and
so,
if
done
sufficient
times,
to
give
the
appearance
of
a
conditioned
reflex
action
having
been
established.
GENERALIZED
LEARNING
PROGRAMS
The
construction
of
a
learning
program
of
the
above
type
presents
no
difficulty
to
anyone
who
is
familiar
with
the
technique
of
programming.
However,
such
a
pro-
gram
makes
it
possible
to
teach
the
machine
only
those
things
which
the
programmer
had
in
mind
when
he
wrote
the
program.
For
example,
the
program
just
described
would
not
enable
the
operator
to
teach
the
machine
to
different
figures
after
alternate
stimuli.
If
the
pro-
grammer
had
wished
to
do
so,
he
could
have
allowed
for
this
possibility
in his
program.
In
fact,
at
the
expense
of
making
the
program
longer
and
more
complicated,
he
could
include
any
number
of
extra
features,
but
obvi-
ously
he
could
not
think
of
every
possible
experiment
which
anyone
might
wish
to
try
on
the
machine.
All
the
programmer
is
doing,
in
fact,
is
to
program
the
action
of
the
machine
as
it
were
at
one
remove;
when
he
writes
the
program
he
visualizes,
if
not
in
complete
de-
tail,
at
any
rate
in
general
terms,
all
the
possible
actions
which
the
machine
can
take
in
response
to
legitimate
ac-
tions
on
the
part
of
the
operator.
Such
programms
are
not,
therefore,
as
interesting
as
at
first
sight
might
appear
from
the
point
of
view
of
this
article.
What
is
wanted
is
a
"generalized"
learning
pro-
gram,
which
would
enable
an
operator
to
teach
the
ma-
chine
anything
he
chose,
whether
the
idea
of
his
doing
so
had
occurred
to
the
programmer
or
not.
I
believe
that
such
a
program
would
not
be
a
mere
elaboration
of
the
simple
learning
programs
which
have
been
constructed
up
to
date
but
would
need
to
be
based
on
some
entirely
new
ideas.
Presumably
the
program
would
modify
and
extend
itself
as
the
learning
process
went
on.
As
I
have
pointed
out,
existing
machines
contain
the
means
for
this
extension;
the
difficulty
is
to
construct
a
program
to
make
use
of
them.
If
such
a
program
could
be
made
then
it
would
be
possible
to
teach
the
machine
in
much
the
same
way
as
a
child
is
taught.
Whether
the
new
ideas
I
have
referred
to
will
be
forth-
coming,
it is
hard
to
say.
Certainly,
for
the
present,
progress
appears
to
be
held
up.
Perhaps
this
will
give
comfort
to
those
who
cannot
bear
the
idea
of
machines
thinking;
on
the
other
hand
it
may
stimulate
others
to
further
effort.
BIBLIOGRAPHY
E.
C.
Berkeley,
"Giant
Brains,"
John
Wiley
&
Sons,
New
York,
N.
Y.;
1949.
A.
G.
Oettinger,
"Programming
a
digital
computer
to
learn,"
Phil.
Mag.,
vol.
7,
no.
43,
pp.
1243-1263;
1952.
C.
E.
Shannon,
"Programming
a
computer
for
playing
chess,"
Ibid.,
vol.
7,
no.
41,
pp.
256-275;
1950.
A.
M.
Turing,
"Computing
machinery
and
intelligence,"
Mind,
vol.
59,
pp.
433-460;
1950.
M.
V.
Wilkes,
"Can
machines
think?"
The
Spectator,
no.
6424,
pp.
177-178;
1951.
"Automatic
calculating
machines,"
Jour.
Roy.
Soc.
A.,
vol.
100,
pp.
56-90;
1951.
M.
V.
Wilkes,
D.
J.
Wheeler,
and
S.
Gill,
"The
Preparation
of
Pro-
grams
for
an
Electronic
Digital
Computer,"
Addison-Wesley
Cambridge,
Mass.;
1951.
Computers
and
Automata*
CLAUDE
E.
SHANNONt,
FELLOW,
IRE
Summary-This
paper
reviews
briefly
some
of
the
recent
de-
velopments
in
the
field
of
automata
and
nonnumerical
computation.
A
number
of
typical
machines
are
described,
including
logic
ma-
chines,
game-playing
machines
and
learning
machines.
Some
theo-
retical
questions
and
developments
are
discussed,
such
as
a
com-
parison
of
computers
and
the
brain,
Turing's
formulation
of
comput-
ing
machines
and
von
Neumann's
models
of
self-reproducing
ma-
chines.
*
Decimal
classification:
621.385.2.
Original
manuscript
received
by
the
Institute,
July
17,
1953.
t
Bell
Telephone
Laboratories,
Murray
Hill,
N.
J.
INTRODUCTION
SOAMUEL
BUTLER,
in
1871,
completed
the
manu-
%
script
of
a
most
engaging
social
satire,
Erewhon.
Three
chapters
of
Erewhon,
originally
appearing
under
the
title
"Darwin
Among
the
Machines,"
are
a
witty
parody
of
The
Origin
of
Species.
In
the
topsy-
turvy
logic
of
satirical
writing,
Butler
sees
machines
as'
gradually
evolving
into
higher
forms.
He
considers
the
classification
of
machines
into
genera,
species
and
vari-
C.
E.
Shannon
first
became
known
for
a paper
in
which
he
applied
Boolean
Algebra
to
relay
switching
circuits;
this
laid
the
foundation
for
the
present
extensive
application
of
Boolean
Algebra
to
computer
design.
Dr.
Shannon,
who
is
engaged
in
mathematical
research
at
Bell
Telephone
Laboratories,
is
an
authority
on
information
theory.
More
recently
he
received
wide
notice
for
his
ingenious
maze-solving
mechanical
mouse,
and
he
is
well-known
as
one
of
the
leading
explorers
into
the
exciting,
but
uncharted
world
of
new
ideas
in
the
computer
field.
The
Editors
asked
Dr.
Shannon
to
write
a
paper
describing
current
experiments,
and
specula-
tions
concerning
future
developments
in
computer
logic.
Here
is
a
real
challenge
for
those
in
search
of
a
field
where
creative
ability,
imagination,
and
curiosity
will
undoubtedly
lead
to
major
advances
in
human
knowledge.-The
Editor
1234
October
Shannon:
Computers
and
Automata
eties,
their
feeding
habits,
their
rudimentary
sense
or-
gans,
their
reproductive
and
evolutionary
mechanisms
(inefficient
machines
force
men
to
design
more
efficient
ones),
tendencies
toward
reversion,
vestigial
organs,
and
even
the
problem
of
free
will
in
machines.
Rereading
Erewhon
today
one
finds
"The
Book
of
the
Machines"
disturbingly
prophetic.
Current
and
pro-
jected
computers
and
control
systems
are
indeed
as-
suming
more
and
more
the
capacities
and
functions
of
animals
and
man,
to
a
far
greater
degree,
in
fact,
than
was
envisaged
by
Butler.
The
bread-and-butter
work
of
large-scale
computers
has
been
the
solution
of
involved
numerical
problems.
To
many
of
us,
however,
the
most
exciting
potentialities
of
computers
lie
in
their
ability
to
perform
non-numer-
ical
operations-to
work
with
logic,
translate
lan-
guages,
design
circuits,
play
games,
co-ordinate
sensory
and
manipulative
devices
and,
generally,
assume
com-
plicated
functions
associated
with
the
human
brain.
Non-numerical
computation
is
by
no
means
an
un-
proven
offspring
of
the
more
publicized
arithmetic
cal-
culation.
The
shoe
is
rather
on
the
other
foot.
A
hun-
dred
years
ago
Charles
Babbage
was
inspired
in
the
design
of
his
remarkably
prescient
analytical
engine
by
a
portrait
woven
in
silk
on
a
card
controlled
Jacquard
loom-a
device
then
in
existence
half
a
century.
The
largest
and
most
reliable
current
information
processing
machine
is
still
the
automatic
telephone
system.
Our
factories
are
filled
with
ingenious
and
unsung
devices
performing
almost
incredible
feats
of
sensing,
processing
and
transporting
materials
in
all
shapes
and
forms.
Rail-
way
and
power
systems
have
elaborate
control
and
pro-
tective
networks
against
accidents
and
human
errors.
These,
however,
are
all
special-purpose
automata.
A
significant
new
concept
in
non-numerical
computation
is
the
idea
of
a
general-purpose
programmed
computer-
a
device
capable
of
carrying
out
a
long
sequence
of
elementary
orders
analogous
to
those
of
a
numerical
computer.
The
elementary
orders,
however,
will
relate
not
to
operations
on
numbers
but
to
physical
motions,
operations
with
words,
equations,
incoming
sensory
data,
or
almost
any
physical
or
conceptual
entities.
This
paper
reviews
briefly
some
of
the
research
in
non-
numerical
computation
and
discusses
certain
of
the
problems
involved.
The
field
is
currently
very
active
and
in
a
short
paper
only
a
few
sample
developments
can
be
mentioned.
THE
BRAIN
AND
COMPUTERS
The
brain
has
often
been
compared,
perhaps
over-
enthusiastically,
with
computing
machines.
It
contains
roughly
1010
active
elements
called
neurons.
Because
of
the
all
or
none
law
of
nervous
action,
neurons
bear
some
functional
resemblance
to
our
binary
computer
elements,
relays,
vacuum
tubes
or
transistors.
The
num-
ber
of
elements
is
six
orders
of
magnitude
greater
than
our
largest
computers.
McCullough
has
picturesquely
put
it
that
a
computer
with
as
many
tubes
as
a
man
has
neurons
would
require
the
Empire
State
building
to
house
it,
Niagara
Falls
to
power
it
and
the
Niagara
river
to
cool
it.
The
use
of
transistors
in
such
a
com-
parison
would
improve
the
figures
considerably,
power
requirements
coming
down
to
the
hundreds
of
kilowatt
range
(the
brain
dissipates
some
25
watts)
and
size
re-
quirements
(with
close
packing)
comparable
to
an
ordi-
nary
dwelling.
It
may
also
be
argued
that
the
increased
speed
of
electronic
components
by
a
factor
of,
say,
10'
might
be
partially
exchangeable
against
equipment
re-
quirements.
Comparisons
of
this
sort
should
be
taken
well
salted
-our
understanding
of
brain
functioning
is
still,
in
spite
of
a
great
deal
of
important
and
illuminating
research,
very
primitive.
Whether,
for
example,
the
neuron
itself
is
the
proper
level
for
a
functional
analysis
is
still
an
open
question.
The
random
structure
at
the
neural
level
in
number,
placement
and
interconnections
of
the
neu-
rons,
suggests
that
only
the
statistics
are
important
at
this
stage,
and,
consequently,
that
one
might
average
over
local
structure
and
functioning
before
constructing
a
mathematical
model.
The
similarities
between
the
brain
and
computers
have
often
been
pointed
out.
The
differences
are
per-
haps
more
illuminating,
for
they
may
suggest
the
im-
portant
features
missing
from
our
best
current
brain
models.
Among
the
most
important
of
these
are:
1.
Differences
in
size.
Six
orders
of
magnitude
in
the
number
of
components
takes
us
so
far
from
our
ordinary
experience
as
to
make
extrapolation
of
function
next
to
meaningless.
2.
Differences
in
structural
organization.
The
appar-
ently
random
local
structure
of
nerve
networks
is
vastly
different
from
the
precise
wiring
of
artificial
automata,
where
a
single
wrong
connection
may
cause
malfunctioning.
The
brain
somehow
is
de-
signed
so
that
overall
functioning
does
not
depend
on
the
exact
structure
in
the
small.
3.
Differences
in
reliability
organization.
The
brain
can
operate
reliably
for
decades
without
really
seri-
ous
malfunctioning
(comparable
to
the
meaning-
less
gibberish
produced
by
a
computer
in
trouble
conditions)
even
though
the
components
are
prob-
ably
individually
no
more
reliable
than
those
used
in
computers.
4.
Differences
in
logical
organization.
The
differences
here
seem
so
great
as
to
defy
enumeration.
The
brain
is
largely
self-organizing.
It
can
adapt
to
an
enormous
variety
of
situations
tolerably
well.
It
has
remarkable
memory
classification
and
access
features,
the
ability
to
rapidly
locate
stored
data
via
numerous
"coordinate
systems."
It
can
set
up
stable
servo
systems
involving
complex
relations
between
its
sensory
inputs
and
motor
outputs,
with
great
facility.
In
contrast,
our
digital
com-
puters
look
like
idiot
savants.
For
long
chains
of
arithmetic
operations
a
digital
computer
runs
cir-
cles
around
the
best
humans.
When
we
try
to
pro-
gram
computers
for
other
activities
their
entire
organization
seems
clumsy
and
inappropriate.
1235
1953
PROCEEDINGS
OF
THE
I.R.E.
5.
Differences
in
input-output
equipment.
The
brain
is
equipped
with
beautifully
designed
input
organs,
particularly
the
ear
and
the
eye,
for
sensing
the
state
of
its
environment.
Our
best
artificial
coun-
terparts,
such
as
Shepard's
Analyzing
Reader
for
recognizing
and
transcribing
type,
and
the
"Audrey"
speech
recognition
system
which
can
recognize
the
speech
sounds
for
the
ten
digits
seem
pathetic
by
comparison.
On
the
output
end,
the
brain
controls
hundreds
of
muscles
and
glands.
The
two
arms
and
hands
have
some
sixty
inde-
pendent
degrees
of
freedom.
Compare
this
with
the
manipulative
ability
of
the
digitally
controlled
milling
machine
developed
at
M.I.T.,
which
can
move
its
work
in
but
three
co-ordinates.
Most
of
our
computers,
indeed,
have
no
significant
sensory
or
manipulative
contact
with
the
real
world
but
operate
only
in
an
abstract
environment
of
num-
bers
and
operations
on
numbers.
TURING
MACHINES
The
basic
mathematical
theory
of
digital
computers
was
developed
by
A.
M.
Turing
in
1936
in
a
classic
paper
"On
Computable
Numbers
with
an
Application
to
the
Entscheidungsproblem."
He
defined
a
class
of
computing
machines,
now
called
Turing
machines,
con-
sisting
basically
of
an
infinite
paper
tape
and
a
comput-
ing
element.
The
computing
element
has
a
finite
number
of
internal
states
and
is
capable
of
reading
from
and
writing
on
one
cell
of
the
tape
and
of
moving
it
one
cell
to
the
right
or
left.
At
a
given
time,
the
computing
ele-
ment
will
be
in
a
certain
state
and
reading
what
is
writ-
ten
in
a
particular
cell
of
the
tape.
The
next
operation
will
be
determined
by
the
current
state
and
the
symbol
being
read.
This
operation
will
consist
of
assuming
a
new
state
and
either
writing
a
new
symbol
(in
place
of
the
one
currently
read)
or
moving
to
the
right
or
to
the
left.
It
is
possible
for
machines
of
this
type
to
compute
numbers
by
setting
up
a
suitable
code
for
interpreting
the
symbols.
For
example,
in
Turing's
formulation
the
machines
final
answers
in
binary
notation
on
al-
ternate
cells
of
the
tape,
using
the
other
cells
for
inter-
mediate
calculations.
It
can
be
shown
that
such
machines
form
an
ex-
tremely
broad
class
of
computers.
All
ordinary
digital
computers
which
do
not
contain
a
random
or
probabil-
istic
element
are
equivalent
to
some
Turing
machine.
Any
number
that
can
be
computed
on
these
machines,
or
in
fact
by
any
ordinary
computing
process,
can
be
computed
by
a
suitable
Turing
machine.
There
are,
however,
as
Turing
showed,
certain
problems
that
can-
not
be
solved
and
certain
numbers
that
cannot
be
com-
puted
by
any
Turing
machine.
For
example,
it
is
not
possible
to
construct
a
Turing
machine
which,
given
a
suitably
coded
description
of
another
Turing
machine,
can
always
tell
whether
or
not
the
second
Turing
ma-
chine
will
continue
indefinitely
to
symbols
in
the
squares
corresponding
to
the
final
answer.
It
may,
at
a
certain
point
in
the
calculation,
relapse
into
an
infinite
intermediate
computation.
The
existence
of
mechan-
ically
unsolvable
problems
of
this
sort
is
of
great
interest
to
logicians.
Turing
also
developed
the
interesting
concept
of
a
universal
Turing
machine.
This
is
a
machine
with
the
property
that
if
a
suitably
coded
description
of
any
Tur-
ing
machine
is
printed
on
its
tape,
and
the
machine
started
at
a
suitable
point
and
in
a
suitable
state,
it
will
then
act
like
the
machine
described,
that
is,
compute
(normally
at
a
much
slower
rate)
the
same
number
that
the
described
machine
would
compute.
Turing
showed
that
such
universal
machines
can
be
designed.
They
of
course
are
capable
of
computing
any
computable
num-
ber.
Most
digital
computers,
provided
they
have
ac-
cess
to
an
unlimited
memory
of
some
sort,
are
equiva-
lent
to
universal
Turing
machines
and
can,
in
principle,
imitate
any
other
computing
machine
and
compute
any
computable
number.
The
work
of
Turing
has
been
generalized
and
reformu-
lated
in
various
ways.
One
interesting
generalization
is
the
notion
of
A
computability.
This
relates
to
a
class
of
Turing
type
machines
which
have
the
further
feature
that
they
can,
at
certain
points
of
the
calculation,
ask
questions
of
a
second
"oracular"
device,
and
use
the
answers
in
further
calculations.
The
oracular
machine
may
for
example
have
answers
to
some
of
the
unsolvable
problems
of
ordinary
Turing
machines,
and
conse-
quently
enable
the
solution
of
a
larger
class
of
problems.
LOGIC
MACHINES
Boolean
algebra
can
be
used
as
a
mathematical
tool
for
studying
the
properties
of
relay
and
switching
cir-
cuits.
Conversely,
it
is
possible
to
solve
problems
of
Boolean
algebra
and
formal
logic
by
means
of
simple
relay
circuits.
This
possibility
has
been
exploited
in
a
number
of
logic
machlines.
A
typical
machine
of
this
kind,
described
by
McCallum
and
Smith,
can
handle
logical
relations
involving
up
to
seven
classes
or
truth
variables.
The
required
relations
among
these
variables,
given
by
the
logical
problem
at
hand,
are
plugged
into
the
machine
by
means
of
a
number
of
"connective
boxes."
These
connective
boxes
are
of
six
types
and
provide
for
the
logical
connectives
"not,"
"and,"
"or,"
"'or
else,"
"if
and
only
if,"
and
"if-then."
When
the
con-
nections
are
complete,
starting
the
machine
causes
it
to
hunt
through
the
27
=
128
combinaticns
of
the
basic
variables,
stopping
at
all
combinations
which
satisfy
the
constraints.
The
machine
also
indicates
the
number
of
"true"
variables
in
each
of
these
states.
McCallum
and
Smith
give
the
following
typical
problem
that
may
be
solved
on
the
machine:
It
is
known
that
salesmen
always
tell
the
truth
and
engi-
neers
always
tell
lies.
G
and
E
are
salesmen.
C
states
that
D
is
an
engineer.
A
declares
that
B
affirms
that
C
asserts
that
D
says
that
E
insists
that
F
denies
that
G
is
a
sales-
man.
If
A
is
an
engineer,
how
many
engineers
are
there?
A
very
suggestive
feature
in
this
machine
is
a
selec-
1236
October
Shannon:
Computers
and
Automata
tive
feedback
system
for
hunting
for
particular
solutions
of
the
logical
equations
without
an
exhaustive
search
through
all
possible
combinations.
This
is
achieved
by
elements
which
sense
whether
or
not
a
particular
logi-
cal
relation
is
satisfied.
If
not,
the
truth
variables
in-
volved
in
this
relation
are
caused
to
oscillate
between
their
two
possible
values.
Thus,
variables
appearing
in
unsatisfied
relations
are
continually
changing,
while
those
appearing
only
in
satisfied
relations
do
not
change.
If
ever
all
relations
are
simultaneously
satisfied
the
machine
stops
at
that
particular
solution.
Changing
only
the
variables
in
unsatisfied
relations
tends,
in
a
general
way,
to
lead
to
a
solution
more
rapidly
than
methodical
exhaustion
of
all
cases,
but,
as
is
usually
the
case
when
feedback
is
introduced,
leads
to
the
pos-
sibility
of
continual
oscillation.
McCallum
and
Smith
point
out
the
desirability
of
making
the
changes
of
the
variables
due
to
the
feedback
unbalance
as
random
as
possible,
to
enable
the
machine
to
escape
from
periodic
paths
through
various
states
of
the
relays.
GAME
PLAYING
MACHINES
The
problem
of
designing
game-playing
machines
is
fascinating
and
has
received
a
good
deal
of
attention.
The
rules
of
a
game
provide
a
sharply
limited
environ-
ment
in
which
a
machine
may
operate,
with
a
clearly
defined
goal
for
its
activities.
The
discrete
nature
of
most
games
matches
well
the
digital
computing
tech-
niques
available
without
the
cumbersome
analog-digital
conversion
necessary
in
translating
our
physical
en-
vironment
in
the
case
of
manipulating
and
sensing
machines.
Game
playing
machines
may
be
roughly
classified
into
types
in
order
of
increasing
sophistication:
1.
Dictionary-type
machines.
Here
the
proper
move
of
the
machine
is
decided
in
advance
for
each
pos-
sible
situation
that
may
arise
in
the
game
and
listed
in'
a
"dictionary"
or
function
table.
When
a
particular
position
arises,
the
machine
merely
looks
up
the
move
in
the
dictionary.
Because
of
the
extravagant
memory
requirements,
this
rather
uninteresting
method
is
only
feasible
for
excep-
tionally
simple
games,
e.g.,
tic-tac-toe.
2.
Machines
using
rigorously
correct
playing
for-
mulas.
In
some
games,
such
as
Nim,
a
complete
mathematical
theory
is
known,
whereby
it
is
pos-
sible
to
compute
by
a
relatively
simple
formula,
in
any
position
that
can
be
won,
a
suitable
winning
move.
A
mechanization
of
this
formula
provides
a
perfect
game
player
for
such
games.
3.
Machines
applying
general
principles
of
approx-
imate
validity.
In
most
games
of
interest
to
hu-
mans,
no
simple
exact
solution
is
known,
but
there
are
various
general
principles
of
play
which
hold
in
the
majority
of
positions.
This
is
true
of
such
games
as
checkers,
chess,
bridge,
poker
and
the
like.
Machines
may
be
designed
applying
such
general
principles
to
the
position
at
hand.
Since
the
principles
are
not
infallible,
neither
are
the
machines,
as
indeed,
neither
are
humans.
4.
Learning
machines.
Here
the
machine
is
given
only
the
rules
of
the
game
and
perhaps
an
elementary
strategy
of
play,
together
with
some
method
of
improving
this
strategy
through
experience.
Among
the
many
methods
that
have
been
sug-
gested
for
incorporation
of
learning
we
have:
a)
trial-and-error
with
retention
of
successful
and
elimination
of
unsuccessful
possibilities;
b)
imitation
of
a
more
successful
opponent;
c)
"teaching"
by
approval
or
disapproval,
or
by
informing
the
machine
of
the
nature
of
its
mis-
takes;
and
finally
d)
self-analysis
by
the
machine
of
its
mistakes
in
an
attempt
to
devise
general
principles.
Many
examples
of
the
first
two
types
have
been
con-
structed
and
a
few
of
the
third.
The
fourth
type,
learn-
ing
game-players,
is
reminiscent
of
Mark
Twain's
com-
ment
on
the
weather.
Here
is
a
real
challenge
for
the
programmer
and
machine
designer.
Two
exanmples
of
the
third
category,
machines
ap-
plying
general
principles,
may
be
of
interest.
The
first
of
these
is
a
machine
designed
by
E.
F.
Moore
and
the
writer
for
playing
a
commercial
board
game
known
as
Hex.
This
game
is
played
on
a
board
laid
out
in
a
regular
hexagon
pattern,
the
two
players
alternately
placing
black
and
white
pieces
in
unoccupied
hexagons.
The
entire
board
forms
a
rhombus
and
Black's
goal
is
to
connect
the
top
and
bottom
of
this
rhombus
with
a
continuous
chain
of
black
pieces.
White's
goal
is
to
con-
nect
the
two
sides
of
the
rhombus
with
a
chain
of
white
pieces.
After
a
study
of
this
game,
it
was
conjectured
that
a
reasonably
good
move
could
be
made
by
the
fol-
lowing
process.
A
two-dimensional
potential
field
is
set
up
corresponding
to
the
playing
board,
with
white
pieces
as
positive
charges
and
black
pieces
as
negative
charges.
The
top
and
bottom
of
the
board
are
negative
and
the
two
sides
positive.
The
move
to
be
made
cor-
responds
to
a
certain
specified
saddle
point
in
this
field.
To
test
this
strategy,
an
analog
device
was
constructed,
consisting
of
a
resistance
network
and
gadgetry
to
lo-
cate
the
saddle
points.
The
general
principle,
with
some
improvements
suggested
by
experience,
proved
to
be
reasonably
sound.
With
first
move,
the
machine
won
about
seventy
per
cent
of
its
games
against
human
op-
ponents.
It
frequently
surprised
its
designers
by
choos-
ing
odd-looking
moves
which,
on
analysis,
proved
sound.
We
normally
think
of
computers
as
expert
at
long
in-
volved
calculations
and
poor
in
generalized
value
judg-
ments.
Paradoxically,
the
positional
judgment
of
this
machine
was
good;
its
chief
weakness
was
in
end-game
combinatorial
play.
It
is
also
curious
that
the
Hex-player
reversed
the
usual
computing
procedure
in
that
it
solved
a
basically
digital
problem
by
an
anlog
machine.
The
game
of
checkers
has
recently
been
programmed
into
a
general-purpose
computer,
using
a
"general
prin-
ciple"
approach.
C.
S.
Strachey
used
a
method
similar
to
1953
1237
PROCEEDINGS
OF
THE
I.R.E.
one
proposed
by
the
writer
for
programming
chess-an
investigation
of
the
possible
variations
for
a
few
moves
and
a
minimax
evaluation
applied
to
the
resulting
posi-
tions.
The
following
is
a
sample
game
played
by
the
checker
program
with
notes
by
Strachey.
(The
white
squares
are
numbered
consecutively,
0-31,
from
left
to
right
and
top
to
bottom.
Numbers
in
parentheses
indi-
cate
captures.)
MACHINE
STRACHEY
11-15
23-18
7-11
21-17
8-12
20-16
a
12-21
(16)
25-16
(21)
9-14
!
b
18-
9
(14)
6-20
(16,
9)
c
27-23
2-
7
d
23-18
5-
8
18-14
8-13
e
17-
8
(13)
4-13
(8)
14-
9
1-Sf
9-
6
15-19
6-
1
(K)
5-9
1-6?g
0-
5
1
h
6-15
(10)
11-25
(22,
15)
30-21
(25)
13-17
21-14
(17)
9-18
(14)
24-21
18-23
26-22
23-27
22-17
5-8
i
17-14
8-13
14-
9
19-23
9-
6
23-26
j
31-22
(26)
27-31
(K)
6-
2
(K)
7-10
2-
7
10-15
21-16
?k
3-10
(7)
16-
9
(13)
10-14
9-
6
15-19
6-
2
(K)
31-27
m
2-
6
27-31
m
6-10
31-26
n
10-17
(14)
19-23
29-25
26-31
p
Notes:
a)
An
experiment
on
my
part-the
only
deliberate
offer
I
made.
I
thought,
wrongly,
that
it
was
quite
safe.
b)
Not
foreseen
by
me.
c)
Better
than
5-21
(9,
17).
d)
A
random
move
(zero
value).
Shows
the
lack
of
a
constructive
plan.
e)
Another
random
move
of
zero
value.
Actually
rather
good.
f)
Bad.
Ultimately
allows
me
to
make
a
King.
10-14
would
would
have
been
better.
g)
A
bad
slip
on
my
part.
h)
Taking
full
advantage
of
my
slip.
i)
Bad,
unblocks
the
way
to
a
King.
j)
Sacrifice
in
order
to
get
a
King
(not
to
stop
me
Kinging).
A
good
move,
but
not
possible
before
19-23
had
been
made
by
chance.
k)
Another
bad
slip
on
my
part.
m)
Purposeless.
The
strategy
is
failing
badly
in
the
end
game.
n)
Too
late.
p)
Futile.
The
game
was
stopped
at
this
point
as
the
outcome
was
obvious.
While
obviously
no
world
champion,
the
machine
is
certainly
better
than
many
humans.
Strachey
points
out
various
weaknesses
in
the
program,
particularly
in
certain
end-game
positions,
and
suggests
possible
im-
provements.
LEARNING
MACHINES
The
concept
of
learning,
like
those
of
thinking,
con-
sciousness
and
other
psychological
terms,
is
difficult
to
define
precisely
in
a
way
acceptable
to
the
various
inter-
ested
parties.
A
rough
formulation
might
be
framed
somewhat
as
follows.
Suppose
that
an
organism
or
a
ma-
chine
can
be
placed
in,
or
connected
to,
a
class
of
en-
vironments,
and
that
there
is
a
measure
of
"success"
or
"adaptation"
to
the
environment.
Suppose
further
that
this
measure
is
comparatively
local
in
time,
that
is,
that
one
can
measure
the
success
over
periods
of
time
short
compared
to
the
life
of
the
organism.
If
this
local
meas-
ure
of
success
tends
to
improve
with
the
passage
of
time,
for
the
class
of
environments
in
question,
we
may
say
that
the
organism
or
machine
is
learning
to
adapt
to
these
environments
relative
to
the
measure
of
success
chosen.
Learning
achieves
a
quantitative
significance
in
terms
of
the
broadness
and
complexity
of
the
class
of
environments
to
which
the
machine
can
adapt.
A
chess
playing
machine
whose
frequency
of
wins
increases
dur-
ing
its
operating
life
may
be
said
by
this
definition
to
be
learning
chess,
the
class
of
environments
being
the
chess
players
who
oppose
it,
and
the
adaptation
meas-
sure,
the
winning
of
games.
A
number
of
attempts
have
been
made
to
construct
simple
learning
machines.
The
writer
constructed
a
maze-solving
device
in
which
an
arbitrary
maze
can
be
set
up
in
a
five-by-five
array
of
squares,
by
placing
partitions
as
desired
between
adjacent
squares.
A
per-
manently
magnetized
"mouse,"
placed
in
the
maze,
blunders
about
by
a
trial
and
error
procedure,
striking
various
partitions
and
entering
blind
alleys
until
it
eventually
finds
its
way
to
the
"food
box."
Placed
in
the
maze
a
second
time,
it
will
move
directly
to
the
food
box
from
any
part
of
the
maze
that
it
has
visited
in
its
first
exploration,
without
errors
or
false
moves.
Placed
in
other
parts
of
the
maze,
it
will
blunder
about
until
it
reaches
a
previously
explored
part
and
from
there
go
directly
to
the
goal.
Meanwhile
it
will
have
added
the
information
about
this
part
of
the
maze
to
its
memory,
and
if
placed
at
the
same
point
again
will
go
directly
to
the
goal.
Thus
by
placing
it
in
the
various
unexplored
parts
of
the
maze,
it
eventually
builds
up
a
complete
pattern
of
information
and
is
able
to
reach
the
goal
di-
rectly
from
any
point.
If
the
maze
is
now
changed,
the
mouse
first
tries
the
old
path,
but
on
striking
a
partition
starts
trying
other
directions
and
revising
its
memory
until
it
eventually
reaches
the
goal
by
some
other
path.
Thus
it
is
able
to
forget
an
old
solution
when
the
problem
is
changed.
The
mouse
is
actually
driven
by
an
electromagnet
moving
beneath
the
maze.
The
motion
of
the
electro-
magnet
is
controlled
by
a
relay
circuit
containing
about
110
relays,
organized
into
a
memory
and
a
computing
circuit,
somewhat
after
that
of
a
digital
computer.
The
maze-solver
may
be
said
to
exhibit
at
a
very
primitive
level
the
abilities
to
(1)
solve
problems
by
trial
and
error,
(2)
repeat
the
solutions
without
the
errors,
(3)
add
and
correlate
new
information to
a
par-
tial
solution,
(4)
forget
a
solution
when
it
is
no
longer
applicable.
1238
October
Shannon:
Computers
and
Automata
Another
approach
to
mechanized
learning
is
that
of
saitably
programming
a
large-scale
computer.
A.
E.
Oettinger
has
developed
two
learning
programs
for
the
Edsac
computer
in
Cambridge,
England.
In
the
first
of
these,
the
machine
was
divided
into
two
parts,
one
part
playing
the
role
of
a
learning
machine
and
the
second
its
environment.
The
environment
represented
ab-
stractly
a
number
of
stores
in
which
various
items
might
be
purchased,
different
stores
stocking
different
classes
of
items.
The
learning
machine
faced
the
problem
of
learning
where
various
items
might
be
purchased.
Start-
ing
off
with
no
previous
knowledge
and
a
particular
item
to
be
obtained,
it
would
search
at
random
among
the
stores
until
the
item
was
located.
When
finally
suc-
cessful,
it
noted
in
its
memory
where
the
article
was
found.
Sent
again
for
the
same
article
it
will
go
directly
to
the
shop
where
it
previously
obtained
this
article.
A
further
feature
of
the
program
was
the
introduction
of
a
bit
of
"curiosity"
in
the
learning
machine.
When
it
succeeded
in
finding
article
number
j
in
a
particular
shop
it
also
noticed
whether
or
not
that
shop
carried
articles
j-
1
and
j+
1
and
recorded
these
facts
in
its
memory.
The
second
learning
program
described
by
Oettinger
is
modeled
more
closely
on
the
conditioned
reflex
be-
havior
of
animals.
A
stimulus
of
variable
intensity
can
be
applied
to
the
machine
in
the
form
of
an
input
in-
teger.
To
this
stimulus
the
machine
may
respond
in
a
number
of
different
ways
indicated
by
an
output
in-
teger.
After
the
response,
it is
possible
for
the
operator
to
indicate
approval
or
disapproval
by
introducing
a
third
integer
at
a
suitable
point.
When
the
machine
starts
operating,
its
responses
to
stimuli
are
chosen
at
random.
Indication
of
approval
improves
the
chances
for
the
response
immediately
preceding;
indication
of
dis-
approval
reduces
this
chance.
Furthermore,
as
a
par-
ticular
response
is
learned
by
conditioning
it
with
ap-
proval,
the
stimulus
required
for
this
response
decreases.
Finally,
there
is
a
regular
decay
of
thresholds
when
no
approval
follows
a
response.
Further
embellishments
of
programs
of
this
sort
are
limited
only
by
the
capacity
of
the
computer
and
the
energy
and
ingenuity
of
the-
program
designer.
Unfor-
tunely,
the
elementary
orders
available
in
most
large-
scale
computers
are
poorly
adapted
to
the
logical
re-
quirements
of
learning
programs,
and
the
machines
are
therefore
used
rather
inefficiently.
It
may
take
a
dozen
or
more
orders
to
represent
a
logically
simple
and
fre-
quently
used
operation
occurring
in
a
learning
routine.
Another
type
of
learning
machine
has
been
con-
structed
by
D.
W.
Hagelbarger.
This
is
a
machine
de-
signed
to
play
the
game
of
matching
pennies
against
a
human
opponent.
On
the
front
panel
of
the
machine
are
a
start
button,
two
lights
marked
+
and
-,
and
a
key
switch
whose
extreme
positions
are
also
marked
+
and
-.
To
play
against
the
machine,
the
player
chooses
+
or
-,
and
then
pushes
the
start
button.
The
machine
will
then
light
up
one
of
the
two
lights.
If
the
machine
matches
the
player,
that
is,
lights
the
light
correspond-
ing
to
the
choice
of
the
player,
the
machine
wins;
other-
wise
the
player
wins.
When
the
play
is
complete,
the
player
registers
by
appropriate
movement
of
the
key
switch
the
choice
he
made.
The
machine
is
so
constructed
as
to
analyze
certain
patterns
in
the
players'
sequence
of
choices,
and
at-
tempt
to
capitalize
on
these
patterns
when
it
finds
them.
For
example,
some
players
have
a
tendency
if
they
have
won
a
round,
played
the
same
thing
and
won
again,
to
then
change
their
choice.
The
machine
keeps
count
of
these
situations
and,
if
such
tendencies
appear,
plays
in
such
a
way
as
to
win.
When
such
patterns
do
not
ap-
pear
the
machine
plays
at
random.
It
has
been
found
the
machine
wins
about
55-60
per
cent
of
the
rounds,
while
by
chance
or
against
an
op-
ponent
that
played
strictly
at
random
it
would
win
only
50
per
cent
of
the
time.
It
appears
to
be
quite
difficult
for
a
human
being
to
produce
a
random
sequence
of
pluses
and
minuses
(to
insure
the
50
per
cent
wins
he
is
entitled
to
by
the
theory
of
games)
and
even
more
difficult
to
actually
beat
the
machine
by
leading
it
on
to
suspect
patterns,
and
then
re-versing
the
patterns.
A
second
penny-matching
machine
was
designed
by
the
writer,
following
the
same
general
strategy
but
using
a
different
criterion
to
decide
when
to
play
at
random
and
when
to
assume
that
an
apparent
behavior
pattern
is
significant.
After
considerable
discussion
as
to
which
of
these
two
machines
could
beat
the
other,
and
fruitless
attempts
to
solve
mathematically
the
very
complicated
statistical
problem
involved
when
they
are
connected
together,
the
problem
was
relegated
to
experiment.
A
third
small
machine
was
constructed
to
act
as
umpire
and
pass
the
information
back
and
forth
between
the
machines
concerning
their
readiness
to
make
a
move
and
the
choices
made.
The
three
machines
were
then
plugged
together
and
allowed
to
run
for
a
few
hours,
to
the
ac-
companiment
of
small
side-bets
and
loud
cheering.
Ironically,
it
turned
out
that
the
smaller,
more
precipi-
tate
of
the
two
machines
consistently
beat
the
larger,
more
deliberate
one
in
a
ratio
of
about
55
to
45.
A
still
different
type
of
learning
machine
was
devised
by
W.
Ross
Ashby
who
christened
it
the
Homeostat.
Homeostasis,
a
word
coined
by
Walter
B.
Cannon,
re-
lates
to
an
animal's
ability
to
stabilize,
by
feedback,
such
biological
variables
as
body
temperature,
chemical
concentrations
in
the
blood
stream,
etc.
Ashby's
device
is
a
kind
of
self-stabilizing
servo
system.
The
first
model
of
the
Homeostat
contained
four
interconnected
servos.
The
cross-connections
of
these
servos
passed
through
four
stepping
switches
and
resistors
connected
to
the
points
of
the
steppers.
Thus
the
effect
of
unbalance
in
the
other
three
loops
on
a
particular
loop
depended
on
the
values
of
the
resistors
being
contacted
by
the
stepper
associated
with
that
loop.
When
any
one
of
the
servos
was
sufficiently
out
of
balance,
a
corresponding
limit
relay
would
operate
and
cause
the
corresponding
step-
ping
switch
to
advance
one
point.
Now
normally,
a
1953
1239
PROCEEDINGS
OF
THE
I.R.E.
servo
system
with
four
degrees
of
freedom
and
random
cross-
and
self-gain
figures
will
not
be
stable.
If
this
occurred,
one
or
more
of
the
stepping
switches
would
advance
and
a
new
set
of
resistors
would
produce
a
new
set
of
gain
figures.
If
this
set
again
proved
unstable,
a
further
advance
of
the
steppers
would
occur
until
a
stable
situation
was
found.
The
values
of
the
resistors
connected
to
the
stepping
switches
were
chosen
by
ran-
dom
means
(using
a
table
of
randon
numbers).
Facilities
were
provided
for
introducing
many
arbitrary
changes
or
constraints
among
the
servos.
For
example,
their
con-
nections
could
be
reversed,
two
of
them
could
be
tied
together,
one
of
them
held
at
a
fixed
value,
etc.
Under
all
these
conditions,
the
mechanism
was
able
to
find
a
suitable
stable
position
with
all
the servos
in
balance.
Considering
the
machine's
goal
to
be
that
of
stabilizing
the
servos,
and
the
environment
to
be
represented
by
the
various
alterations
and
constraints
introduced
by
the
operator,
the
Homeostat
may
be
said
to
adapt
to
its
environment.
Certain
features
of
the
Homeostat
are
quite
attrac-
tive
as
a
basis
for
learning
machines
and
brain
models.
It
seems
in
certain
ways
to
do
a
bit
more
than
was
ex-
plicitly
designed
into
it.
For
example,
it
has
been
able
to
stabilize
under
situations
not
anticipated
when
the
machine
was
constructed.
The
use
of
randomly
chosen
resistors
is
particularly
suggestive
and
reminiscent
of
the
random
connections
among
neurons
in
the
brain.
Ashby,
in
fact,
believes
that
the
general
principle
em-
bodied
in
the
Homeostat,
which
he
calls
ultra-stability,
may
underlie
the
operation
of
the
animal
nervous
sys-
tem.
One
of
the
difficulties
of
a
too
direct
application
of
this
theory
is
that,
as
Ashby
points
out,
the
time
required
for
finding
a
stable
solution
grows
more
or
less
exponentially
with
the
number
of
degrees
of
free-
dom.
With
only
about
20
degrees
of
freedom,
it
would
require
many
lifetimes
to
stabilize
one
system.
At-
tempts
to
overcome
this
difficulty
lead
to
rather
in-
volved
conceptual
constructions,
so
involved
that
it
is
extremely
difficult
to
decide
just
how
effectively
they
would
operate.
Our
mathematical
tools
do
not
seem
sufficiently
sharp
to
solve
these
problems
and
further
experimental
work
would
be
highly
desirable.
SELF-REPRODUCING
MACHINES
In
Erewhon
the
reproduction
process
in
machines
was
pictured
as
a
kind
of
symbiotic
co-operation
between
man
and
machines,
the
machines
using
man
as
an
inter-
mediary
to
produce
new
machines
when
the
older
ones
were
worn
out.
Man's
part
is
akin
to
that
of
the
bee
in
the
fertilization
of
flowers.
Recently
von
Neumann
has
studied
at
an
abstract
level
the
problem
of
true
self-
reproduction
in
machines,
and
has
formulated
two
dif-
ferent
mathematical
models
of
such
"machines."
The
first
of
these
may
be
pictured
somewhat
as
fol-
lows.
"Machines"
in
the
model
are
constructed
from
a
small
number
(of
the
order
of
twenty)
types
of
ele-
mentary
components.
These
components
have
relatively
simple
functions,
for
example,
girders
Tor
structural
pur-
poses,
elementary
logical
elements
similar
to
simplified
relays
or
neurons
for
computing,
sensing
components
for
detecting
the
presence
of
other
elements,
joining
components
(analogous
to
a
soldering
iron)
for
fastening
elements
together,
and
so
on.
From
these
elements,
vari-
ous
types
of
machines
may
be
"constructed."
In
particu-
lar,
it
is
possible
to
design
a
kind
of
universal
construc-
tion
machine,
analogous
to
Turing's
universal
comput-
ing
machine.
The
universal
constructing
machine
can
be
fed
a
sequence
of
instructions,
similar
to
the
program
of
a
digital
computer,
which
describe
in
a
suitable
code
how
to
construct
any
other
machine
that
can
be
built
with
the
elementary
components.
The
universal
con-
structing
machine
will
then
proceed
to
hunt
for
the
needed
components
in
its
environment
and
build
the
machine
described
on
its
tape.
If
the
instructions
to
the
universal
constructing
machine
are
a
description
of
the
universal
constructing
machine
itself,
it
will
proceed
to
build
a
copy
of
itself,
and
would
be
a
self-reproducing
machine
except
for
the
fact
that
the
copy
is
not
yet
supplied
with
a
set
of
instructions.
By
adding
to
the
uni-
versal
machine
what
amounts
to
a
tape-copying
device
and
a
relatively
simple
controlling
device,
a
true
self-
reproducing
machine
is
obtained.
The
instructions
now
describe
the
original
universal
machine
with
the
addi-
tion
of
the
tape
reproducer
and
the
controlling
device.
The
first
operation
of
the
machine
is
to
reproduce
this
entity.
The
controlling
device
then
sends
the
instruction
tape
through
the
tape
reproducer
to
obtain
a
copy,
and
places
this
copy
in
the
second
machine.
Finally,
it
turns
the
second
machine
on,
which
starts
reading
its
instructions
and
building
a
third
copy,
and
so
ad
in-
finitum.
More
recently,
von
Neumann
has
turned
from
this
somewhat
mechanical
model
to
a
more
abstract
self-
reproducing
structure-one
based
on
a
two-dimensional
array
of
elementary
"cells."
Each
cell
is
of
relatively
simple
internal
structure,
having,
in
fact,
something
like
thirty
possible
internal
states,
and
each
cell
communi-
cates
directly
only
with
its
four
neighbors.
The
state
of
a
cell
at
the
next
(quantized)
step
in
time
depends
only
on
the
current
state
of
the
cell
and
the
states
of
its
four
neighbors.
By
a
suitable
choice
of
these
state
transitions
it
is
possible
to
set
up
a
system
yielding
a
kind
of
self-
reproducing
structure.
A
group
of
contiguous
cells
can
act
as
an
organic
unit
and
operate
on
nearby
quiescent
cells
in
such
a
way
as
to
organize
a
group
of
them
into
an
identical
unit.
This
second
model
avoids
many
of
the
somewhat
extraneous
problems
of
locating,
recognizing
and
posi-
tioning
components
that
were
inherent
in
the
first
model,
and
consequently
leads
to
a
simpler
mathemati-
cal
formulation.
Furthermore,
it
has
certain
analogies
with
various
chemical
and
biological
problems,
such
as
those
of
crystal
and
gene
reproduction,
while
the
first
model
is
more
closely
related
to
the
problem
of
large
scale
animal
reproduction.
1240
October
Shannon:
Computers
and
Automata
An
interesting
concept
arising
from
both
models
is
the
notion
of
a
critical
complexity
required
for
self-repro-
duction.
In
either
case,
only
sufficiently
complicated
"machines"
will
be
capable
of
self-reproduction.
Von
Neumann
estimates
the
order
of
tens
of
thousands
of
components
or
cells
to
obtain
this
property.
Less
com-
plicated
structures
can
only
construct
simpler
"ma-
chines"
than
themselves,
while
more
complicated
ones
may
be
capable
of
a
kind
of
evolutionary
improvement
leading
to
still
more
complicated
organisms.
CHALLENGE
TO
THE
READER
We
hope
that
the
foregoing
sample
of
non-numerical
computers
may
have
stimulated
the
reader's
appetite
for
research
in
this
field.
The
problem
of
how
the
brain
works
and
how
machines
may
be
designed
to
simulate
its
activity
is
surely
one
of
the
most
important
and
difficult
facing
current
science.
Innumerable
questions
demand
clarification,
ranging
from
experimental
and
development
work
on
the
one
hand
to
purely
mathe-
matical
research
on
the
other.
Can
we
design
significant
machines
where
the
connections
are
locally
random?
Can
we
organize
machines
into
a
hierarchy
of
levels,
as
the
brain
appears
to
be
organized,
with
the
learning
of
the
machine
gradually
progressing
up
through
the
hier-
archy?
Can
we
program
a
digital
computer
so
that
(eventually)
99
per
cent
of
the
orders
it
follows
are
written
by
the
computer
itself,
rather
than
the
few
per
cent
in
current
programs?
Can
a
self-repairing
machine
be
built
that
will
locate
and
repair
faults
in
its
own
components
(including
components
in
the
maintenance
part
of
the
machine)?
What
does
a
random
element
add
in
generality
to
a
Turing
machine?
Can
manipulative
and
sensory
devices
functionally
comparable
to
the
hand
and
eye
be
developed
and
coordinated
with
com-
puters?
Can
either
of
von
Neumann's
self-reproducing
models
be
translated
into
hardware?
Can more
satis-
factory
theories
of
learning
be
formulated?
Can
a
ma-
chine
be
constructed
which
will
design
other
machines,
given
only
their
broad
functional
characteristics?
What
is
a
really
good
set
of
orders
in
a
digital
computer
for
general
purpose
non-numerical
computation?
How
can
a
computer
memory
be
organized
to
learn
and
remem-
ber
by
association,
in
a
manner
similar
to
the
human
brain?
We
suggest
these
typical
questions,
and
the
entire
automata
field,
as
a
challenge
to
the
reader.
Here
is
research
territory
ripe
for
scientific
prospectors.
It
is
not
a
matter
of
reworking
old
operations,
but
of
locat-
ing
the
rich
new
veins
and
perhaps
in
some
cases
merely
picking
up
the
surface
nuggets.
BIBLIOGRAPHY
W.
R.
Ashby,
Design
for
a
Brain
(New
York,
Wiley,
1951).
E.
C.
Berkeley,
Giant
Brains,
or
Machines
That
Think
(New
York,
Wiley,
1949).
S.
Butler,
Erewhon
and
Erewhon
Revisited
(New
York,
Modern
Library
Edition,
1927).
J.
Diebold,
Automation
(New
York,
Van
Nostrand,
1952).
A.
S.
Householder
and
H.
D.
Landahl,
Mathematical
Biophysics
of
the
Central
Nervous
System
(Bloomington,
Principia
Press,
1945)
pp.
103-1
10.
S.
C.
Kleene,
Representation
of
Events
in
Nerve
Nets
and
Finite
Auto-
mata,
Rand
Corporation
Memorandum
RM-704,
1951.
D.
M.
McCallum
and
J.
B.
Smith,
"Mechanized
Reasoning,"
Elec-
tronic
Engineering
(April,
1951).
Warren
S.
McCulloch,
and
Walter
Pitts,
"A
Logical
Calculus
of
the
Ideas
Immanent
in
Nervous
Activity,"
Bull.
Math.
Biophysics,
(1943)
vol.
5,
pp.
115-133.
W.
S.
McCulloch,
"The
Brain
as
a
Computing
Machine,"
Electrical
Engineering
(June,
1949).
John
Meszar,
"Switching
Svstems
as
Mechanical
Brains
Bell
Labs.
Record,
(1953)
vol.
31,
pp.
63-69.
A.
Oettinger,
"Programming
a
Digital
Computer
to
Learn,"
Phil.
Mag.,
(December,
1952)
vol.
43,
pp.
1243-1263.
W.
Pease,
"An
Automatic
Machine
Tool,"
Scientific
American,
(Sep-
tember,
1952)
vol.
187,
pp.
101-115.
C.
E.
Shannon,
Presentation
of
a
Maze-Solving
Machine,
Transactions
of
the
Eighth
Cvbernetics
Conference,
Josiah
Macy,
Jr.
Founda-
tion,
New
York,
1952,
pp.
173-180.
C.
E.
Shannion,
"Programming
a
Computer
for
Playing
Chess,"
Phil.
Mag.,
(March,
1950)
vol.
41,
pp.
256-275.
C.
S.
Strachey,
"Logical
or
Non-Mathematical
Programmes,"
Proc.
of
the
Assn.for
Computing
Machinery,
Toronto
(1952),
pp.
46-49.
A.
M.
Turing,
"Computing
Machinery
and
Intelligence,"
Mind,
(1950)
vol.
59,
pp.
433-460.
A.
M.
Turing,
On
Computable
Numbers,
with
an
Application
to
the
Entscheidungsproblem,
Proc.
Lond.
Math.
Soc.,
(1936)
vol.
24,
pp.
230-265.
J.
Von
Neuman,
"The
General
and
Logical
Theory
of
Auitomata
from
Cerebral
Mechanisms
in
Behavior,"
(New
York,
Wiley,
1951,
pp.
1-41.
J.
Von
Neumann,
Probabilistics
Logics,
California
Institute
of
Tech-
nology,
1952.
N.
Wiener,
Cybernetics
(New
York,
Wiley,
1948).
C..\.5D
1953
1241